Holographic entanglement entropy probes (non)locality

Abstract

We study the short-distance structure of geometric entanglement entropy in certain theories with a built-in scale of nonlocality. In particular we examine the cases of Little String Theory and Noncommutative Yang-Mills theory, using their AdS/CFT descriptions. We compute the entanglement entropy via the holographic ansatz of Ryu and Takayanagi to conclude that the area law is violated at distance scales that sample the nonlocality of these models, being replaced by an extensive volume law. In the case of the noncommutative model, the critical length scale that reveals the area/volume law transition is strongly affected by UV/IR mixing effects. We also present an argument showing that Lorentz symmetry tends to protect the area law for theories with field-theoretical density of states.

24 pages and 8 figures; added references, corrected some typos and added a full NEW SECTION with an explicit result linking holography, Lorentz invariance and area law of entanglement entropy

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